I am using the PID block in Simulink and limiting the output to (+/-)5. The plant becomes unstable and untunable after putting these limits. The plant is stable and tuneable otherwise if no limits are applied. The output from the PID tuner goes beyond 10 when no limits are applied and I want to limit the output to 5.
Not all systems are tunable in all ranges. You can find via the Nyquist plot the stability ranges for the ranges of a gain the system can be stable. This can be plotted and analyzed in matlab.
H = tf([2 5 1],[1 2 3]); nyquist(H)